Learn on PengiBig Ideas Math, Course 2Chapter 1: Integers

Lesson 5: Dividing Integers

In this Grade 7 lesson from Big Ideas Math, Course 2, Chapter 1, students learn the rules for dividing integers, including how to determine whether a quotient is positive, negative, or zero based on the signs of the two integers. Students discover that dividing two integers with the same sign yields a positive quotient, while dividing integers with different signs yields a negative quotient. The lesson connects integer division to multiplication and applies these rules to solving real-life problems, aligning with standards MAFS.7.NS.1.2b and MAFS.7.NS.1.3.

Section 1

Division as the Inverse of Multiplication

Property

Division is the inverse operation of multiplication. We check our answer to division by multiplying the quotient by the divisor to determine if it equals the dividend.

Examples

To solve $56 \div 7$ , we can think 'what number times 7 equals 56?'. The answer is 8. Check: $8 \cdot 7 = 56$ .
To solve $\frac{48}{8}$ , we can think 'what number times 8 equals 48?'. The answer is 6. Check: $6 \cdot 8 = 48$ .
To solve $54 \div 9$ , we can think 'what number times 9 equals 54?'. The answer is 6. Check: $6 \cdot 9 = 54$ .

Explanation

Division and multiplication are opposites that undo each other. You can use your multiplication facts to solve division problems and to check if your answer is correct. It's a great way to be sure you have the right quotient!

Section 2

Quotients of Signed Numbers

Property

The quotient of two numbers with opposite signs is a negative number.
The quotient of two numbers with the same sign is a positive number.
If $a$ is any nonzero number, then

\frac{0}{a} = 0 \quad \text{and} \quad \frac{a}{0} \text{ is undefined.}

Examples

The quotient of two numbers with the same sign is positive: $\frac{-45}{-9} = 5$ .

The quotient of two numbers with opposite signs is negative: $32 \div (-4) = -8$ .

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Division as the Inverse of Multiplication

Property

Division is the inverse operation of multiplication. We check our answer to division by multiplying the quotient by the divisor to determine if it equals the dividend.

Examples

To solve $56 \div 7$ , we can think 'what number times 7 equals 56?'. The answer is 8. Check: $8 \cdot 7 = 56$ .
To solve $\frac{48}{8}$ , we can think 'what number times 8 equals 48?'. The answer is 6. Check: $6 \cdot 8 = 48$ .
To solve $54 \div 9$ , we can think 'what number times 9 equals 54?'. The answer is 6. Check: $6 \cdot 9 = 54$ .

Explanation

Section 2

Quotients of Signed Numbers

Property

The quotient of two numbers with opposite signs is a negative number.
The quotient of two numbers with the same sign is a positive number.
If $a$ is any nonzero number, then

\frac{0}{a} = 0 \quad \text{and} \quad \frac{a}{0} \text{ is undefined.}

Examples

The quotient of two numbers with the same sign is positive: $\frac{-45}{-9} = 5$ .

The quotient of two numbers with opposite signs is negative: $32 \div (-4) = -8$ .

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Division as the Inverse of Multiplication

Property

Division is the inverse operation of multiplication. We check our answer to division by multiplying the quotient by the divisor to determine if it equals the dividend.

Examples

To solve $56 \div 7$ , we can think 'what number times 7 equals 56?'. The answer is 8. Check: $8 \cdot 7 = 56$ .
To solve $\frac{48}{8}$ , we can think 'what number times 8 equals 48?'. The answer is 6. Check: $6 \cdot 8 = 48$ .
To solve $54 \div 9$ , we can think 'what number times 9 equals 54?'. The answer is 6. Check: $6 \cdot 9 = 54$ .

Explanation

Section 2

Quotients of Signed Numbers

Property

The quotient of two numbers with opposite signs is a negative number.
The quotient of two numbers with the same sign is a positive number.
If $a$ is any nonzero number, then

\frac{0}{a} = 0 \quad \text{and} \quad \frac{a}{0} \text{ is undefined.}

Examples

The quotient of two numbers with the same sign is positive: $\frac{-45}{-9} = 5$ .

The quotient of two numbers with opposite signs is negative: $32 \div (-4) = -8$ .